72.15.13 problem 24

Internal problem ID [14815]
Book : DIFFERENTIAL EQUATIONS by Paul Blanchard, Robert L. Devaney, Glen R. Hall. 4th edition. Brooks/Cole. Boston, USA. 2012
Section : Chapter 3. Linear Systems. Review Exercises for chapter 3. page 376
Problem number : 24
Date solved : Thursday, March 13, 2025 at 04:19:29 AM
CAS classification : [[_2nd_order, _missing_x]]

\begin{align*} y^{\prime \prime }+2 y^{\prime }+5 y&=0 \end{align*}

With initial conditions

\begin{align*} y \left (0\right )&=3\\ y^{\prime }\left (0\right )&=-1 \end{align*}

✓ Maple. Time used: 0.016 (sec). Leaf size: 20

ode:=diff(diff(y(t),t),t)+2*diff(y(t),t)+5*y(t) = 0; 
ic:=y(0) = 3, D(y)(0) = -1; 
dsolve([ode,ic],y(t), singsol=all);
 

\[ y = {\mathrm e}^{-t} \left (\sin \left (2 t \right )+3 \cos \left (2 t \right )\right ) \]

✓ Mathematica. Time used: 0.019 (sec). Leaf size: 22

ode=D[y[t],{t,2}]+2*D[y[t],t]+5*y[t]==0; 
ic={y[0]==3,Derivative[1][y][0] ==-1}; 
DSolve[{ode,ic},y[t],t,IncludeSingularSolutions->True]
 

\[ y(t)\to e^{-t} (\sin (2 t)+3 \cos (2 t)) \]

✓ Sympy. Time used: 0.168 (sec). Leaf size: 17

from sympy import * 
t = symbols("t") 
y = Function("y") 
ode = Eq(5*y(t) + 2*Derivative(y(t), t) + Derivative(y(t), (t, 2)),0) 
ics = {y(0): 3, Subs(Derivative(y(t), t), t, 0): -1} 
dsolve(ode,func=y(t),ics=ics)
 

\[ y{\left (t \right )} = \left (\sin {\left (2 t \right )} + 3 \cos {\left (2 t \right )}\right ) e^{- t} \]